Tracking a Moving Object in Log-Polar Mapped Coordinates

Abstract

A new visual method with log-polar imaging geometry is proposed for tracking an object that translates in three dimensional space. The log-polar mapping is a popular model for space-variant sensing in computer vision, and is efficient in data reduction so that a tracking system can work with real time operation. An active camera with three degree of freedom (pan, tilt and zoom) is used to track the object and the log-polar mapping of images is performed with software computation, in which we can change the conversion parameters. In the log-polar coordinates, the lateral component of the object’s translation varies sinusoidally, while the longitudinal motion component along the visual axis is reduced to rather simpler translation. These motion components can be estimated in sub-pixel order of accuracy by detecting the phase difference of the complex wavelet transforms of the converted image sequences. By using a commercially available PC without additional peripheral equipment, the pursuit of a moving planar object can be executed in the rate of 10 or 15 frames/sec.